Bellwork

1
Bellwork
Clickers

• Multiply
• Ruby is standing in her back yard and she decides
  to estimate the height of a tree. She stands so
  that the tip of her shadow coincides with the top
  of the trees shadow. Ruby is 66 inches tall.
  The distance from the tree to Ruby is 95 feet and
  the distance between the tip of the shadows and
  ruby is 7 feet.
• What postulate or theorem can you use to show
  that the triangles in the diagram are similar?
• About how tall is the tree, to the nearest foot?
• What if? Curtis is 75 inches tall. At a
  different time of day, he stands so that the tip
  of the his shadow and the tip of the trees
  shadow coincide, as described above. His shadow
  is 6 feet long. How far is Curtis from the tree?

2
Bellwork Solution

• Multiply

3
Bellwork Solution

• Ruby is standing in her back yard and she decides
  to estimate the height of a tree. She stands so
  that the tip of her shadow coincides with the top
  of the trees shadow. Ruby is 66 inches tall.
  The distance from the tree to Ruby is 95 feet and
  the distance between the tip of the shadows and
  ruby is 7 feet.
• What postulate or theorem can you use to show
  that the triangles in the diagram are similar?
• About how tall is the tree, to the nearest foot?
• What if? Curtis is 75 inches tall. At a
  different time of day, he stands so that the tip
  of the his shadow and the tip of the trees
  shadow coincide, as described above. His shadow
  is 6 feet long. How far is Curtis from the tree?

4
Use Proportionality Theorems

• Section 6.6

5
Test on Thursday
6
The Concept

• Yesterday we finished our exploration of the
  different methodologies to prove similarity in
  triangles
• Today were going to see some theorems that allow
  us to name proportionality within triangles and
  parallel lines

7
Theorems
Theorem 6.4 Triangle Proportionality Theorem If
a line parallel to one side of a triangle
intersects the other two sides, then it divides
the two sides proportionally
Theorem 6.5 Converse of the Triangle
Proportionality Theorem If a line divides two
sides of a triangle proportionally, then it is
parallel to the third side.
B
D
E
C
A
8
Example
Solve for x, if DE and AC are parallel
B
12
x
D
E
20
15
C
A
9
Example
What value of x makes the lines parallel?
16
13
32.5
x
10
Example
What value of x makes the lines parallel?
6
x3
8x-1
18
11
Example
What value of x makes the lines parallel?
x
5
15x
27
12
In your notes
A cross brace is added to an A-Frame tent. Why
is the brace not parallel to the ground?
x3
In your notes and in complete sentences, write
two sentences that explains your answer
15
16
25
24
13
Theorems
Theorem 6.6 If three parallel lines intersect
two transversals, then they divide the
transversals proportionally
A
B
C
14
Example
Theorem 6.6 If three parallel lines intersect
two transversals, then they divide the
transversals proportionally
51
x
15
42
15
Example
What value of x makes the lines parallel?
16
x
15
20
16
Example
What value of x makes the lines parallel?
x2
x
12
19
17
Example
What value of x makes the lines parallel?
x2
2
x-5
4
18
Theorems
Theorem 6.7 If a ray bisects an angle of a
triangle, then it divides the opposite side into
segments whose lengths are proportional to the
lengths of the other two sides.
B
E
A
C
19
Example
Solve for x, if Ray AE bisects ?ABC.
B
8
24
E
x
A
32
C
20
Example
Find x if BC40
B
x
24
E
A
36
C
21
Homework

• 6.6
• 1, 2-36 even

22
HW
23
Most Important Points

• Triangle Proportionality Theorems